Final answer:
The question involves measuring an object's dimensions with a ruler and calculating surface area or volume with significant figures. It emphasizes the importance of estimation and uncertainty in measurements, which affects accuracy when reporting final calculations in significant figures.
Step-by-step explanation:
The question pertains to the measurement of objects and the calculation of their surface area or volume with a specified degree of accuracy. When using a ruler to measure an object's dimensions, such as width or length, we can achieve a certain level of precision based on the smallest divisions on the ruler. For example, if an object measures more than 1 cm but less than 2 cm, and the ruler's divisions allow for it, we can record the measurement as 1.25 cm or 1.36 cm, depending on the estimated portion between the tick marks. This principle also applies to calculating volumes, such as a rectangular box with sides of 1.80 cm, 2.05 cm, and 3.1 cm. The measurement of each side is accompanied by an uncertainty, such as ±0.05 cm, which must be considered when calculating the total volume and its associated uncertainty.
Significant figures are vital when reporting measured values. For instance, when multiplying two measured numbers, the number of significant figures in the result is determined by the measurement with the fewest significant figures. Significant figures influence how we round our final answer. As another example, the multiplication of 0.6238 cm and 6.6 cm results in 4.11708 cm², which we round to 4.1 cm² to maintain two significant figures.